Compressive Sensing is a recently developed technique that exploits the sparsity of naturally occurring signals and images to solve inverse problems when the number of samples is less than the size of the original signal. We apply this technique to solve underdetermined inverse problems that commonly occur in remote sensing, including superresolution, image fusion and deconvolution. We use l1-minimization to develop algorithms that perform as well as or better than conventional methods for these problems. Our algorithms use a library of samples from similar images or a model for the image to be reconstructed to express the image as a sparse linear combination. A set of feature vectors is generated from the library or basis and is used to find the sparsest linear combination that matches the data using l1-minimization.
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